The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Combinatorics, Probability and Computing
A simple solution to the k-core problem
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
Hamiltonicity of random graphs produced by 2-processes
Random Structures & Algorithms
The diameter of sparse random graphs
Random Structures & Algorithms
The critical phase for random graphs with a given degree sequence
Combinatorics, Probability and Computing
The probability that a random multigraph is simple
Combinatorics, Probability and Computing
A critical point for random graphs with a given degree sequence
Random Structures & Algorithms
Karp-sipser on random graphs with a fixed degree sequence
Combinatorics, Probability and Computing
The scaling window for a random graph with a given degree sequence
Random Structures & Algorithms
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Let Δ 1 be a fixed positive integer. For \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}{\textbf{ {z}}} \in \mathbb{R}_+^\Delta\end{align*} \end{document} **image** let Gz be chosen uniformly at random from the collection of graphs on ∥z∥1n vertices that have zin vertices of degree i for i = 1,…,Δ. We determine the likely evolution in continuous time of the SIR model for the spread of an infectious disease on Gz, starting from a single infected node. Either the disease halts after infecting only a small number of nodes, or an epidemic spreads to infect a linear number of nodes. Conditioning on the event that more than a small number of nodes are infected, the epidemic is likely to follow a trajectory given by the solution of an associated system of ordinary differential equations. These results also give the likely number of nodes infected during the course of the epidemic and the likely length in time of the epidemic. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 © 2012 Wiley Periodicals, Inc.